This invention is generally related to a lithographic process, and more particularly to a method for correcting optical proximity effects using the radius of curvature of shapes imprinted on a mask.
The advent of advanced lithographic techniques and the attempt of chip manufacturers to closely follow Moore""s law predicting an exponential growth of number of components on a chip and their shrinkage on the wafer is making the process of designing tools for automating the chip design extremely challenging. The chip is imprinted by means of optical lithographic techniques on the silicon wafer by way of chrome on glass masks. As the components on the chip become smaller, they are now on the verge of reaching the limits of capacity of the lithographic process. The non-linearities associated with this lithographic process of imprinting and the laws of physics associated with light (including diffraction of light waves) makes impressing highly unpredictable. For instance, rectangles are foreshortened into elliptical-shapes, right angles are rounded, and the width of the shapes shrinks. In addition to the non-linearity associated with the optical effects, the process of developing after exposing the wafer and the photo-resist thereon also adds to the uncertainty associated with the critical dimensions of the features. Other effects mainly related to the exposure and development effect associated with the resist exist that contribute to the distortions. The combination of these effects are known as optical proximity effects.
To counter the problem of optical proximity, mask designers intentionally and systematically distort the original shapes on the mask. The net result of these distortions is that the imprinted shape on the wafer ultimately looks like the target or intended images, satisfying the design rules that were created to increase the yield in chip manufacturing. These methods are generally referred to as optical proximity corrections (OPC) and can be categorized into three classes:
Ad-hoc Method: This method is almost as old as manufacturing VLSI chips. Early designers modified existing methods by putting xe2x80x98flaresxe2x80x99 and xe2x80x98hammer headsxe2x80x99 at the end of lines and xe2x80x98serifsxe2x80x99 at the rectangular corners to compensate for xe2x80x98line-end shorteningxe2x80x99 and xe2x80x98corner-roundingxe2x80x99 due to process irregularities. Since at this stage the size of the features is still large compared to the wavelength of the light used in the lithographic process, the optical proximity does not contribute significantly to the total error budget of the chip manufacturing. However, as the size of the features continuously shrinks, mask designers have continuously readapted earlier techniques to obtain the desired results. Therefore, though prevalent in the early part of the history of optical proximity effect corrections, there is not record of any further development regarding this tool.
Rules Based Method: This method is an initial attempt to formalize the above ad-hoc method. It was observed by chip designers that any compensation required by a particular shape on the wafer is dependent on neighboring shapes, e.g., an isolated line requires more compensation than a set of dense lines. The rules-based method formalizes this notion in a quantitative way. For example, a chip designer may use the tool to decide what the dimensions of a xe2x80x98hammer-headxe2x80x99 added to compensate for line-end shortening should be or what xe2x80x98corner-serifsxe2x80x99 compensate for corner-rounding. These dimensions can be applied as a function of certain rules as, for instance, those that depend on those of the particular shape to which it is applied, the distance to the neighbors, and the dimensions of the neighbors.
Model Based Method: This method emulates the physical and optical effects that are mostly responsible for shape deformations. At the heart of these methods is a computer simulation program that, given the appropriate optical and physical parameters and the original dimension of the object on the mask, predicts with a certain degree of accuracy the printed dimension of the object on the wafer. In the correction phase of the optical proximity effects, the shape on the mask is iteratively modified so that the output result closely approximates what is desired. Finally, this method deforms existing shapes to achieve the target dimensions.
Accordingly, it is an object of the present invention to correct the problems caused by optical proximity effects in a lithographic process.
It is another object to recognize that optical proximity effects are low-pass filter in nature and to take full advantage of this recognition by better controlling the critical dimensions of the shapes on a mask.
It is still another object to make image less susceptible to low-pass filtering effects and make it possible to achieve a high fidelity printing on the mask.
It is yet another object to replace all the sides or vertices of each shape on the mask having a high radius of curvature with mask patterns having a smaller radius of curvature.
These and other objects of the invention are achieved by providing a method for correcting proximity effects on a mask used in a lithographic process that includes the steps of: providing at least one curved shape to approximate the contour of a polygon on the mask, the polygon controlling the contour of the at least one curved shape; defining the curved shape by way of a plurality of radii of curvature; assigning to each side of the polygon one of the radii of curvature; and modifying the radius of curvature at each of the sides of the polygon until each of the radius of curvature reaches the maximum allowable limit for the side, this maximum allowable limit being determined from stored values of radii of curvature corresponding to a plurality of predetermined curved shapes.
The radius of curvature of each of the sides of the polygon is determined by the low pass filter effect of the lithographic process, wherein the low pass filter effect eliminates the high frequency components associated with the vertices (or sides) forming the polygon.
In another aspect of the invention there is provided a method for correcting proximity effects on a mask used in a lithographic process, that includes the steps of: providing a predetermined polygon of the mask; assigning a curved segment for each side of the predetermined polygon; measuring the radius of curvature of each of the curved segments; mapping the radius of curvature to each side of the polygon; modifying the radius of curvature at each arc of the curve until the radius of curvature respectively reaches a predetermined limit for the arc; and forming a closed shape that approximates the predetermined polygon by joining the curves corresponding to adjacent sides of the predetermined polygon.
The closed curved shapes thus obtained is approximated by linear segments having an orthogonal (i.e., parallel to either the x or y axis), or orthogonal-45 (i.e., parallel to 45 or 135 degree lines) orientation, hereinafter referred to as Ortho and Ortho-45.
Unlike conventional methods, e.g., the xe2x80x98rules based methodxe2x80x99, the present method incorporates the model effects in the process, and unlike the model based effect, the invention is non-iterative and, hence, much faster.